Actual OpenLDAP configuration would be to place B (and maybe B1)
certificate in TLSCACertificateFile/Path element, to be able to verify
the Client certificate. The Server must also place A1 in this element,
so it can be sent to the Client to help it verify the Server
certificate.

So, during the TLS negotiation, B, A1, maybe B1, maybe A are sent to
the Client for it to verify the Server certificate? (remember, this
certificate is signed by A1, and A must already be known by the
Client). That's a waste of bandwidth.

The TLS library doesn't do anything so stupid, it only sends the
certificates that are part of the chain from the subject's cert up to
the root CA.

I think the real question here is if the CA chain that the server sends
and the CA chain that the server uses to verify client certificates can
be different.
In Apache, this is done with the SSLCertificateChainFile and
SSLCACertificateFile directives. This makes it possible to have the
server send a certificate chain that differs from the CAs it uses to
verify clients. This is useful if you want to have a server certificate
signed by one CA, but only accept client certificates signed by another CA.
This sounds like an OpenLDAP feature request to me.

Think about why you would configure such a setup, and what it actually means.
When you have a certificate of your own, signed by a particular CA, that
obviously means that you must trust that CA. If you're going to accept a cert
from another party that is signed by a different CA that obviously means that
you must also trust the other CA. There is absolutely nothing gained from
isolating these two CAs, on either side of the session.

OpenSSL (e.g.) already sends only the chain of certificates relevant to its
own subject cert. The fact that all CAs are tossed into a single file (or
directory) together is irrelevant; in memory it's all managed as a database
and only the certs that it needs are accessed.

If there were indeed anything to be gained by such a feature, it would also
need to be implemented on clients. Look around - do any web browsers allow you
to isolate CAs like this?